### Abstract

Using the results of the "exact" shell-model calculation of McGrory et al. for the Ca isotopes as "experimental data", we performed model calculations for ^{50}Ca in order to test the convergence properties of different perturbation schemes for computing the effective interaction V. As such, our aim was not to describe the physical spectrum of ^{50}Ca. Three different model spaces were investigated: (i) p_{ 3 2} (ii) p_{ 3 2} + p_{ 1 2} and (iii) p_{ 3 2} + p_{ 1 2} + f_{ 5 2}. In the p_{ 3 2} model space three different first-order interactions were used in computing the perturbation expansion for V through third order: (a) V ≡ {G + G}_{3p-1hKB}, (b) a standard G-matrix computed from V in (a), and (c) a doubly partitioned G-matrix computed from V by excluding excitations into the p_{ 1 2}level. The results for the doubly partitioned G yielded the best convergence through third order and the best agreement with the J = 0, T = 1 ground state of ^{50}Ca. The core polarization was found to be repulsive for a pure T = 1 system, so that certain third-order terms did not cancel against the large vertex renormalization terms in our special case. The [2, 1] padé approximant for each interaction appeared to indicate reasonable convergence in all three cases through third order. The results for the expanded (p_{ 3 2} + p_{ 1 2}) and (p_{ 3 2} + p_{ 1 2} + f_{ 5 2}) model spaces were difficult to interpret in a meaningful way, because of small energy denominators. Our results would indicate that one should compute in a doubly partitioned space when there are single-particle levels lying close in energy to the model space levels.

Original language | English (US) |
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Pages (from-to) | 429-440 |

Number of pages | 12 |

Journal | Nuclear Physics, Section A |

Volume | 248 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1975 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

^{50}Ca and the convergence properties of the perturbation expansion for the effective interaction.

*Nuclear Physics, Section A*,

*248*(3), 429-440. https://doi.org/10.1016/0375-9474(75)90522-9